RESEARCH INTERESTS

Ersin Özuğurlu

Current Research

Applied Mathematics: Vortex interactions in quasi-geostrophic flow

I have been working with Dr. Jean N. Reinaud and Prof. David G. Dritschel at the University of St Andrews, St Andrews, Scotland ((http://www-vortex.mcs.st-and.ac.uk) .

Previous experiences

Postdoctoral Research

Applied Mathematics: Effect of magnetic field in the Czochralski growth of silicon crystals

I demonstrated my excellent research abilities by applying an optimization technique for controlling transport phenomena in the Czochralski Silicon crystal growth process with MASTRAPP2d (Multizone Adaptive Scheme for Transport Phase-change Processes.) MASTRAPP2d utilizes a multi-zone adaptive grid-generation technique MAGG for discretizing the physical domain and a curvilinear finite volume ( CFV) technique for solving the governing equations.  The MAGG algorithm distributes grid nodes adaptively in response to the development of the solution and according to the evolution of the problem domain. Further details on the numerical methodology of MASTRAPP2d are provided by Hui Zhang (http://me.eng.sunysb.edu/zhang/Zhang.htm) and Vish Prasad (http://me.eng.sunysb.edu/prasad/Prasad.htm)

My postdoctoral research focused on Czochralski growth of silicon crystals. The application of a magnetic field in a Czochralski crystal growing from an electrically conducting melt has become a well-known technique for improving the crystal quality. It has been experimentally established that a magnetic field can stabilize or even suppress the convection in the melt, which together improves the interface conditions thus reduces the growth striations. Moreover, the appropriate application of a magnetic field allows control of the oxygen concentration in silicon crystals.

Practical experience has shown that strong flow fields in the melted crystal can cause crystal irregularities. Flaws in the crystal can only be detected at the end of the crystal growth process. However the flow field is directly observable experimentally, and can be reliably determined computationally. This suggests that one way to improve crystal would be to control the vorticity.

This work was presented in the annual meeting of DARPA/AFOSR (Defense Advanced Research Project Agency / Air Force Office of Scientific Research) http://thermsa.eng.sunysb.edu Consortium for Crystal Growth Research in New York and is ready for the journal submission. By working as a member of DARPA/AFOSR CCGR, I have augmented my rigorous knowledge of theory with practical experience.

Graduate Research Applied Mathematics: Free-surface problems

In my dissertation, "Effect of variable surface tension on free-surface problems,"

I accomplished three main objectives:

  • Found a better approach for distortion of a two-dimensional bubble (or drop) in a corner flow of an inviscid incompressible fluid by using the series truncation method. This work was published by the European Journal of Applied Mathematics (2000), vol 11, pp. 171-179.

  • Considered the problem of periodic gravity-capillary waves propagating at a constant velocity at the surface of a fluid of infinite depth taking into consideration of variable surface tension and finding that there are many different families of solutions, and these solutions generalize the classical theory of gravity-capillary waves with constant surface tension. Also, an asymptotic solution is presented for a particular distribution of variable surface tension. This work was accepted by the Journal of Engineering Mathematics
    • .

  • Investigated variable surface tension for the two-dimensional free-surface flow due to a pressure distribution moving at a constant velocity at the surface of a fluid of infinite depth and observing that the flow approaches a solitary wave with oscillatory tail, as the pressure tends toward zero.